tell me the easiest way to get a relationship model for query builder?

you need to use whereHas for filter data from relationship table assume you have set plan as relationship function inside Product model so you code will be like this

$results = Product::where('name', 'like', '%'. $request->input('search-product-name'). '%')
    ->whereHas("plan", function ($q) use ($request) {
        $q->where('name', 'like', '%'. $request->input('search-product-plan'). '%');
    })->get();

ref link https://laravel.com/docs/8.x/eloquent-relationships#querying-relationship-existence